However, he has warned the Spaniard he could face a long wait.
Lindegaard has played United's last three games, with De Gea seemingly paying the price for a poor performance in the 3-2 home defeat to Blackburn.
And although the Dane is full of praise for his rival, he has no plans to give up his place in the side lightly.
Asked if he thought De Gea could one day be the best in the world, Lindegaard said: "Of course I do. He has extraordinary attributes, extremely explosive and powerful.
"He is only 21. His potential is massive and there is no doubt he will be United's best goalkeeper at some point.
"My job is to make sure it is not until I have retired. Which is in 10 years."
Quoted in several national newspapers, Lindegaard added: "I am very proud of what I have made out of this.
"Three years ago I was in Denmark's second division. Nobody knew my name. When I first came here nobody could pronounce it.
"It has been fantastic to this point and right now is not the time to relax about it, but to keep pushing on, to get better and to get the best for yourself and the club.
"It is the first time I have played three games in a row and that is what I want, to play as much as possible, but I don't need a definition of my position.
"I am doing everything I can to help David. I enjoy working with him."
Meanwhile, United defender Nemanja Vidic has backed his team-mates to enjoy their traditionally strong finish to the season and retain the Premier League title.
United have been badly hit by injuries and currently trail Manchester City by three points, but Vidic - who has been ruled out for the rest of the season - told BBC North West Tonight: "I'm positive.
"We've had problems with injuries but it seems all the players are getting back and getting fitter. We will be better than we were in the first half of the season.
"It's not bad for the city of Manchester to have two teams competing for the title - as long as we finish in first place."